arXiv research

Investigates fluid flow perturbations using geometric theory.

Introduces a new geometric framework for non-perturbative BV-theory.

New framework robustly handles outliers in Wasserstein DRO for better decision-making.

SGD converges with perturbed forward-backward passes, explained by geometric amplification.

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturba…

Eigenvalues of Steklov eigenproblems change predictably with boundary tweaks.

New geometric interpretation explains over-parameterized models and adversarial perturbations.

Study of free particle's geometry and its perturbations using complex projective structures.

We study the relationship between Bar-Natan's perturbation in Khovanov homology and Szabo's geometric spectral sequence, and construct a link invariant that generalizes both into a common theory. We study a few properties of the new invariant, and introduce a family of s-invariants from the new theory in the same spiri…

Self-similar solutions to geometric flows are stable under small perturbations.

Study local perturbations of vector bundles with polynomial curvature solutions.

We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted Hölder spaces.

Generic smooth minimal hypersurfaces exist in 8D manifolds.

New method proves inequalities for self-shrinkers using perturbation.

Paper analyzes FTPL's effectiveness in combinatorial semi-bandit problems.

Given a state-of-the-art deep neural network classifier, we show the existence of a universal (image-agnostic) and very small perturbation vector that causes natural images to be misclassified with high probability. We propose a systematic algorithm for computing universal perturbations, and show that state-of-the-art …

New proof of Schwarzschild stability using geometric gauge.

The state-of-the-art performance of deep learning algorithms has led to a considerable increase in the utilization of machine learning in security-sensitive and critical applications. However, it has recently been shown that a small and carefully crafted perturbation in the input space can completely fool a deep model.…

Topological parallax assesses AI models' geometric similarity to datasets for safety.

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical investigation, we show that state-of-t…

Geometrically studies Moore-Penrose inverse and polar decomposition continuity.

Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, ther…

Analyzes perturbed contact instantons with Legendrian boundary conditions using geometric analysis.

New framework for gravitational perturbations of Kerr spacetimes, focusing on stability.

In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We conjectured (and proved for the case of $2$-loops) that, after adding counterterms of the expecte…

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C^*-algebra, the La…

Study of mean curvature flow with obstacles using singular perturbation.

Geometric focusing affects dispersive estimates for Schrödinger and wave equations.

The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal co…

Spectral clustering for geometric graphs achieves strong consistency in community recovery.

We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to obtain $A_{\infty}$ algebra structures and some canonically defined deformations of s…

Superconvergence of differential structure on discretized surfaces is studied in this paper. The newly introduced geometric supercloseness provides us with a fundamental tool to prove the superconvergence of gradient recovery on deviated surfaces. An algorithmic framework for gradient recovery without exact geometric i…

New method improves solving combinatorial optimization problems with smoothed policies.

New quantum invariant is asymptotically multiplicative under cyclic covers.

PRoA assesses deep learning robustness against practical functional perturbations.

Formally equates two quantization methods and constructs non-commutative algebras.

Survey on Allen-Cahn equations and systems, focusing on multiplicity results and geometric interpretation.

We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associated, via the so-called clutching map. To this end we adapt to our fra…

State-of-the-art machine learning models frequently misclassify inputs that have been perturbed in an adversarial manner. Adversarial perturbations generated for a given input and a specific classifier often seem to be effective on other inputs and even different classifiers. In other words, adversarial perturbations s…

The paper studies invariant complex manifolds in holomorphic slow-fast systems.

In this paper we study the behaviour of the continuous spectrum of the Laplacian on a complete Riemannian manifold of bounded curvature under perturbations of the metric. The perturbations that we consider are such that its covariant derivatives up to some order decay with some rate in the geodesic distance from a fixe…

WassersteinGrad improves weather forecasting explanations by addressing geometric misalignment issues.

PGEL learns embeddings to diversify protein motifs while maintaining biological function.

Geometric technique determines exactness of SDP robustness certificate.

We present a geometric proof of the averaging theorem for perturbed dynamical systems on a Riemannian manifold, in the case where the flow of the unperturbed vector field is periodic and the $\mathbb{S}^{1}$-action associated to this vector field is not necessarily trivial. We generalize the averaging procedure \cite{A…

The paper calculates how random changes affect paths on a complex geometric space.

A new method compares synthetic power networks to actual ones using multiscale flat norm.

This paper improves FTPL algorithm for semi-bandit problems with best-of-both-worlds guarantees.